Householder operator
In linear algebra, the Householder operator is defined as follows. Let be a finite dimensional inner product space with inner product and unit vector. Then
is defined by
This operator reflects the vector across a plane given by the normal vector.
It is also common to choose a non-unit vector, and normalize it directly in the Householder operator's expressionProperties
The Householder operator verifies the following properties:
Over a real or complex vector space, the Householder operator is also known as the Householder transformation.
